1,720,975 research outputs found
Determinants of Sums of Normal Matrices
No full textRecent efforts in matrix theory have been concerned with describing invariants of matrices with "nice" properties. In this dissertation, we address a conjecture on the determinant of the sum of a pair of normal matrices. Reducing this conjecture to the problem of providing non-negative solutions for a system of linear equations without full rank, we use tools from representation theory and combinatorics to describe the modifications required to provide such solutions, and we suggest a statistical approach to the problem more broadly
Intersection Structures on Secants of Grassmannians
Get PDFRestricted secant varieties of Grassmannians are constructed from sums of points corresponding to k-planes with the restriction that their intersection has a prescribed dimension. This thesis calculates dimensions of restricted, cyclic, and path geometric secants of Grassmannians and relate them to the analogous question for secants of Grassmannians via an incidence variety construction. Next, it defines a notion of expected dimension and gives a formula, which holds if the BDdG conjecture on non-defectivity of Grassmannians is true, for the dimension of all restricted secant varieties of Grassmannians. It also demonstrates example calculations in Macaulay 2 and points out ways to make these calculations more efficient. The thesis also shows a potential application to coding theory
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
The Utilization of Geometric Hashing Techniques for Feature Association during Ground Vehicle Localization
Get PDFThis thesis presents a new approach to laser-based robot localization using the concept of geometric hashing. The technique operates on an a priori feature map representing the navigation environment by recording all possible feature combinations as transformation-invariant sets. Each combination can be defined by an implementation-specific geometric basis, and then hashed in order to promote rapid parallelizable search conditions and easily encode large quantities of information.
The primary focus of this work is centered on the individual component of map data association within the much larger localization pipeline. At this step, the navigation system is generally required to provide a correct association between features extracted in real-time from the environment and their corresponding a priori mapped counterparts. In addition to the main concerns of accuracy and reliability, this thesis addresses several other relevant challenges present in feature-based localization such as time complexity, sensitivity to noise, and the detection of map symmetries.
The concept of using geometric hashing for laser-based localization consists of three phases: the training phase, screening phase, and recognition phase. Within this work, each phase is thoroughly defined and analyzed. Particular attention is given toward the utilization of cylindrical-like features found predominantly in urban environments for use during localization. A simulation was developed to test and verify geometric hashing localization in both unique and ambiguous environments. The results validated that geometric hashing localization can provide sub-meter level accuracy even in the presence of ambiguous geometries so long as sufficient information is present. To test the approach on time-critical scenarios, an implementation of the data association algorithm written C++ was integrated into an existing localization framework deployed on a vehicle. Results showed that the positioning solution is capable of providing sub-meter accuracy at 20 Hz update rates driving through urban environments
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Border Ranks of Monomials
Get PDFYoung flattenings, introduced by Landsberg and Ottaviani, give determinantal equations for secant varieties and their non-vanishing provides lower bounds for border ranks of tensors and in particular polynomials. We study monomial-optimal shapes for Young flattenings, which exhibit the limits of the Young flattening method. In particular, they provide the best possible lower bound for large classes of monomials including all monomials up to degree 6, monomials in 3 variables, and any power of the product of variables. On the other hand, for degree 7 and higher there are monomials for which no Young flattening can give a lower bound that matches the conjecturally tight upper bound of Landsberg and Teitler.There is a technical error in the proof, which I hope to eventually correc
ExteriorExtensions: A package for Macaulay2
Get PDFWe explain a Macaulay2 implementation of a construction, which appeared in [Holweck-Oeding arXiv:2206.13662], of a graded algebra structure on the direct sum of a Lie algebra (typically ) and a -module (typically a subspace of an exterior algebra ). We implement brackets, a Killing form, matrix representations of adjoint operators and ranks of blocks of their powers.Revised document. Code in ancillary file
An Introduction to Bernstein-Gel’fand-Gel’fand Correspondence
Get PDFThis master's thesis serves as an introduction to the Bernstein-Gel'fand-Gel'fand correspondence first written in 1978. We shall cover some of the fundamental objects that the reader may not be familiar with, mainly tensor algebras and adjunction between categories. Finally, we prove the Bernstein-Gel'fand-Gel'fand correspondence for the case of complexes of graded modules as stated in Eisenbud-Fløystad-Schreyer, fleshing out all of the details
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